A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-Norm Fidelity

Fang Li; Stanley Osher; Jing Qin; Ming Yan

doi:10.1007/s10915-016-0183-z

A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-Norm Fidelity

Fang Li, Stanley Osher, Jing Qin, Ming Yan

Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.

Original language	English
Pages (from-to)	82-106
Number of pages	25
Journal	Journal of Scientific Computing
Volume	69
Issue number	1
DOIs	https://doi.org/10.1007/s10915-016-0183-z
State	Published - Oct 1 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Funding

The research of F. Li was supported by the 973 Program 2011CB707104 and the Science and Technology Commission of Shanghai Municipality (STCSM) 13dz2260400, the research of S. Osher and J. Qin was supported by ONR Grants N00014120838 and N00014140444, NSF Grants DMS-1118971 and CCF-0926127, and the Keck Foundation, the research of M. Yan was supported by NSF Grants DMS-1317602. The work was done when the first author was visiting UCLA Department of Mathematics.

Funders	Funder number
National Science Foundation (NSF)	0926127, 1317602, CCF-0926127, 1118971, 1440415, DMS-1118971
Office of Naval Research	N00014140444, N00014120838
W. M. Keck Foundation	DMS-1317602
Science and Technology Commission of Shanghai Municipality	13dz2260400

Keywords

ADMM
Fuzzy membership function
Image segmentation
L1-norm
Segmentation accuracy

ASJC Scopus subject areas

Software
General Engineering
Computational Mathematics
Theoretical Computer Science
Applied Mathematics
Numerical Analysis
Computational Theory and Mathematics

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10.1007/s10915-016-0183-z

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AB - In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.

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A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-Norm Fidelity

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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